Homology of Analytic Sheaves and Duality Theorems

1. Analytic Sheaves.- 1. Preliminary Information.- 2. Injectivity Test.- 3. Local Duality.- 4. Injective and Global Dimension.- 5. Properties of Fine Sheaves.- 2. Homology Theory.- 1. Sheaves of Germs of Homology.- 2. Homology Groups.- 3. Connection with the Functors Ext.- 4. Poincaré Duality.- 5. Dualizing Complexes.- 3. Duality Theorems.- 1. Homology of Coverings.- 2. Cohomology with Arbitrary Supports.- 3. Cohomology with Compact Supports.- 4. Holomorphically Complete Spaces.- 5. Leray Spectral Sequence.- 4. Local Homology.- 1. Homology of a Closed Set.- 2. Local Homology.- 3. Duality Theorems.- 4. Inductive and Projective Limits.- 5. Tests for Separatedness.- 5. Applications.- 1. Dimension of Support.- 2. Homological Codimension.- 3. The Results of Andreotti-Grauert.- 4. Lefschetz Theorem.- 5. Theory of Hyperfunctions.- Notes.- References.